CAUTION: This response got longer than I intended
Biggest benefit is the saving of time and energy. You only have to warm-up once and you don’t need to set up multiple stations. There’s also a focus element: you key in on ONE movement for the entire day. Your mind is set, cues are figured out, you’re dialed in. As a beginner, that’s absolutely ideal.
Physically, it makes it so that you accumulate a significant degree of fatigue in that session. The main work isn’t challenging, the supplemental work isn’t challenging, but added together, it’s challenging. Alternating movements is the “easy” way, because you get to shift the emphasis of the fatigue in between the main and the supplemental. I feel it’s the primary reason people who run BBB and alternate the main and supplemental report the workouts being “too easy”. Doing 5x10 with 50% of your TM isn’t all that challenging when you’re “fresh”, but doing it right after doing your main work will suddenly make it taxing.
And on that part above, if you’re doing main and supplemental, it really is “immediately after”. Unless you intentionally choose to lollygag, you can just hit your top set of the main work, strip the bar down to your supplemental work and get going. When you alternate, unless you own the gym and plan ahead, there’s going to be longer downtime between teardown and set-up.
I understand the argument that, when you alternate the movements, you get more practice frequency, but in my mind 5/3/1 is about getting bigger, stronger, faster and better conditioning: NOT getting better at lifting weights. In a bit of comedy, when it comes to getting bigger and stronger, we actually want to be WORSE at lifting: not better. When we improve our proficiency with the lift, we learn how to recruit more muscles into it, perfect the stroke of the movement, reduce ROM (not cut it short, but make the ROM more efficient), etc etc. All the things that are great for moving maximal poundages in a competition but NOT for creating the greatest possible stress/strain on our system to promote growth.
So in that regard, I don’t see a necessary benefit to getting more practice in the lifts as far as 5/3/1 goes. Inefficient technique will STILL promote muscular growth. And regarding “hitting the muscle groups” with a certain frequency: assistance work and conditioning takes care of that.